%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP019+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:11:29 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : ITP019+1 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.09/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 18:20:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(s_type, type, (
% 0.12/0.38 s: ( $i * $i ) > $i)).
% 0.12/0.38 tff(c_2Ecomplex_2Ecomplex__of__num_2E1_type, type, (
% 0.12/0.38 c_2Ecomplex_2Ecomplex__of__num_2E1: $i > $i)).
% 0.12/0.38 tff(c_2Enum_2E0_2E0_type, type, (
% 0.12/0.38 c_2Enum_2E0_2E0: $i)).
% 0.12/0.38 tff(tyop_2Enum_2Enum_type, type, (
% 0.12/0.38 tyop_2Enum_2Enum: $i)).
% 0.12/0.38 tff(tyop_2Epair_2Eprod_type, type, (
% 0.12/0.38 tyop_2Epair_2Eprod: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tyop_2Erealax_2Ereal_type, type, (
% 0.12/0.38 tyop_2Erealax_2Ereal: $i)).
% 0.12/0.38 tff(tptp_fun_V0z_2E0_3_type, type, (
% 0.12/0.38 tptp_fun_V0z_2E0_3: $i)).
% 0.12/0.38 tff(c_2Ecomplex_2Ecomplex__inv_2E1_type, type, (
% 0.12/0.38 c_2Ecomplex_2Ecomplex__inv_2E1: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 ((~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 ((~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 ((~![V0z_2E0: $i] : ((~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) => (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))) <=> (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(~![V0z_2E0: $i] : ((~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) => (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ecomplex_2ECOMPLEX__INV__NZ')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.12/0.38 tff(9,plain,(
% 0.12/0.38 ~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))),
% 0.12/0.38 inference(or_elim,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))),
% 0.12/0.38 inference(or_elim,[status(thm)],[10])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))) | (~(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) | (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 12, 11])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (^[V0z_2E0: $i] : refl(((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0))))) <=> ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,axiom,(![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm_2Ecomplex_2ECOMPLEX__INV__EQ__0')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,(
% 0.12/0.38 ![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[19])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![V0z_2E0: $i] : ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))) | ((s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__inv_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3))) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))) <=> (s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), V0z_2E0!3) = s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal, tyop_2Erealax_2Ereal), c_2Ecomplex_2Ecomplex__of__num_2E1(s(tyop_2Enum_2Enum, c_2Enum_2E0_2E0)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[22, 21, 14])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------